A320766 Number of ordered set partitions of [n] where the maximal block size equals ten.

1, 22, 528, 12584, 308308, 7843836, 208111904, 5767576672, 167004507384, 5050066185736, 159340977018652, 5240336900883084, 179428070995076904, 6388579669849124748, 236257342145458744968, 9064169856705631376280, 360365153529146965326270

Offset: 10

Author

Alois P. Heinz, Oct 20 2018

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 10..426

Crossrefs

Column k=10 of A276922.

Cf. A276929, A276930.

Programs

Maple

b:= proc(n, k) option remember; `if`(n=0, 1, add(
      b(n-i, k)*binomial(n, i), i=1..min(n, k)))
    end:
a:= n-> (k-> b(n, k) -b(n, k-1))(10):
seq(a(n), n=10..30);

Formula

E.g.f.: 1/(1-Sum_{i=1..10} x^i/i!) - 1/(1-Sum_{i=1..9} x^i/i!).

a(n) = A276930(n) - A276929(n).